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1. 18 Aug 2018 | Technique Narratives | Contributor(s): Swarn Singh

It is not always possible to solve a differential equation analytically.This material makes an effort to teach the basics of numerical methods for first order differential equations by following graphical and numerical approaches. Here we also discuss the order of accuracy of the methods and...

2. 18 Aug 2018 | Technique Narratives | Contributor(s): Suruchi Singh

The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Here we learn to solve a heat equation numerically. It is difficult to study the behavior of temperature in problems with interfaces analytically so...

3. 18 Aug 2018 | Technique Narratives | Contributor(s): Suruchi Singh

The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Here we learn to solve a heat equation numerically. It is difficult to study the behavior of temperature in problems with interfaces analytically so...

4. 18 Aug 2018 | Modeling Scenarios | Contributor(s): Natali Hritonenko

The assignment considers two well-known models of population growth, Verhulst-Pearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or S-shape. The assignment contains two opposite, but related tasks:...

5. 18 Aug 2018 | Modeling Scenarios | Contributor(s): Natali Hritonenko

The assignment considers two well-known models of population growth, Verhulst-Pearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or S-shape. The assignment contains two opposite, but related tasks:...

6. 17 Aug 2018 | Modeling Scenarios | Contributor(s): Therese Shelton

We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

7. 17 Aug 2018 | Modeling Scenarios | Contributor(s): Therese Shelton

We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

8. 15 Aug 2018 | Modeling Scenarios | Contributor(s): Therese Shelton

We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This simple activity can be used to introduce differential...

9. 15 Aug 2018 | Modeling Scenarios | Contributor(s): Therese Shelton

We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a reaction in the language of pharmacokinetics -- the study of how drugs move in the body. This simple activity can be used to introduce differential equations, and it can...

10. 15 Aug 2018 | Modeling Scenarios | Contributor(s): Therese Shelton

We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zero-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This simple activity can be used to introduce differential equations and it can be used to...

11. 15 Aug 2018 | Modeling Scenarios | Contributor(s): Therese Shelton

We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zero-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body. This simple activity can be used to introduce differential equations and it can be used to...

12. 15 Aug 2018 | Modeling Scenarios | Contributor(s): Shinemin Lin

Many students fear the term “Differential Equations.”  They think it is scary mathematics.  In this project I want to use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel. That means even students with...

13. 15 Aug 2018 | Modeling Scenarios | Contributor(s): Shinemin Lin

In this project we use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel.

14. 14 Aug 2018 | Modeling Scenarios | Contributor(s): Richard Spindler

An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...

15. 14 Aug 2018 | Modeling Scenarios | Contributor(s): Richard Spindler

An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...

16. 12 Aug 2018 | Modeling Scenarios | Contributor(s): Meredith Greer

17. 12 Aug 2018 | Modeling Scenarios | Contributor(s): Meredith Greer

Given a system of differential equations, how do the solution graphs compare with the graphs of the differential equations? Students tackle this question using SIR models for well-known infectious diseases. The students view graphs both of solution curves and of the differential equations in the...

18. 12 Aug 2018 | Modeling Scenarios | Contributor(s): Mary Vanderschoot

19. 12 Aug 2018 | Modeling Scenarios | Contributor(s): Mary Vanderschoot

In this project, students develop two SIS models to study eviction trends in a population of non-homeowner households using an actual eviction rate. (The Eviction Lab at Princeton University has developed a nationwide database of evictions based on 83 million eviction records.) As the first...

20. 29 Jul 2018 | Free Online Texts | Contributor(s): Mohammed K A Kaabar

In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, and Applications of Differential Equations. In...